Character eyes are black
It is hard to see it all without all the pictures packed (or I just don't have HDR activated), or that the head is lacking materials. However, I myself have had a few troubles in regards to things being not lit the way I like it. One of the things involves having specularity spots on eyes even in a dimly lit room. The two options I came up with was having "virtual lights" (spot and point) surrounding the face, and having a starfield texture added as emission.

I have played around a bit with your node setup, and what I've come up with is that from the Mix node that is connected to the Principled's Base Color, add a connection to a Bright/Contrast node, connect that to an Ambient Occlusion shader, and then an Add shader that adds together the Principled and Ambient outputs to the Material Output.

With the Bright/Contrast node you can control how bright/vibrant you want your eye, seeing as AO (and Add) doesn't have a slider for how much it affects the material. If you want a "strength slider" for the shader, or don't mind the eye emitting some light, you can exchange the AO shader for an Emission shader.

Hope this helps.